A proof that all elements of a list satisfy a property. It is a list of
proofs, corresponding element-wise to the List
.
A proof that some element of a list satisfies some property
the property to be satsified
Given a decision procedure for a property, decide whether all elements of
a list satisfy it.
the property
the decision procedure
the list to examine
Given a decision procedure for a property, determine if an element of a
list satisfies it.
the property to be satisfied
the decision procedure
the list to examine
Eliminator for Any
No element of an empty list satisfies any property
Given a proof of membership for some element, extract the property proof for it
If there does not exist an element that satifies the property, then it is
the case that all elements do not satisfy.